Question

In: Statistics and Probability

2.58 Companies of the world Refer to Exercise 1.118 (page 61), where we examined data collected...

2.58 Companies of the world

Refer to Exercise 1.118 (page 61), where we examined data collected by the World Bank on the numbers of companies that are incorporated and listed on their country's stock exchange at the end of the year. In Exercise 2.10, you examined the relationship between these numbers for 2012 and 2002, and in Exercise 2.27, you found the correlation between these two variables.

INCCOM

  1. Find the least-squares regression equation for predicting the 2012 numbers using the 2002 numbers.
  2. Sweden had 332 companies in 2012 and 278 companies in 2002. Use the least-squares regression equation to find the predicted number of companies in 2012 for Sweden.
  3. Find the residual for Sweden.
CountryName Country Code N1992 N2002 N2012
Uganda UGA 3 10
Tanzania TZA 5 17
Papua New Guinea PNG 8 11
Zambia ZMB 11 20
Malta MLT 12 20
Namibia NAM 3 13 7
Lebanon LBN 13 10
Uruguay URY 26 14 6
Estonia EST 14 16
Botswana BWA 11 18 24
Barbados BRB 15 19 24
Bermuda BMU 22 13
Kyrgyz Republic KGZ 22 18
Costa Rica CRI 93 23 9
Ghana GHA 15 24 34
United Arab Emirates ARE 24 102
Panama PAN 13 26 25
West Bank and Gaza PSE 27 47
Bolivia BOL 30 40
Trinidad and Tobago TTO 28 31 37
Ecuador ECU 65 31 45
El Salvador SLV 31 64
Slovenia SVN 35 61
Cote d'Ivoire CIV 27 38 37
Mauritius MUS 22 40 87
Jamaica JAM 48 42 36
Bahrain BHR 42 43
Luxembourg LUX 59 46 29
Tunisia TUN 17 47 59
Hungary HUN 23 48 51
Kazakhstan KAZ 49 74
Lithuania LTU 51 33
Paraguay PRY 54 62
Morocco MAR 62 55 76
Iceland ISL 57 11
Kenya KEN 57 57 57
Venezuela, RB VEN 91 59 41
Latvia LVA 62 31
Ireland IRL 62 42
Portugal PRT 191 63 46
Croatia HRV 2 66 184
Saudi Arabia SAU 60 68 158
Zimbabwe ZWE 62 76 76
Czech Republic CZE 78 17
Macedonia, FYR MKD 78 32
Argentina ARG 175 83 101
Kuwait KWT 85 189
Austria AUT 112 91 70
Oman OMN 60 96 124
Nepal NPL 98 216
Serbia SRB 99 1086
Colombia COL 80 114 76
New Zealand NZL 123 131 142
Belgium BEL 171 143 154
Finland FIN 61 147 119
Cyprus CYP 39 154 111
Jordan JOR 103 158 243
Armenia ARM 161 12
Mexico MEX 195 166 131
Norway NOR 115 179 184
Netherlands NLD 187 180 105
Ukraine UKR 184 198
Denmark DNK 257 193 174
Nigeria NGA 153 195 192
Russian Federation RUS 26 196 276
Peru PER 287 202 213
Poland POL 16 216 844
Philippines PHL 169 235 268
Sri Lanka LKA 190 238 287
Bangladesh BGD 145 239 229
Chile CHL 245 254 225
Switzerland CHE 180 258 238
Sweden SWE 205 278 332
Georgia GEO 282 133
Turkey TUR 145 288 405
Italy ITA 228 295 279
Iran, Islamic Rep. IRN 118 327 284
Indonesia IDN 155 331 459
Greece GRC 129 341 267
Slovak Republic SVK 354 69
Bulgaria BGR 354 387
Thailand THA 305 398 502
Brazil BRA 565 399 353
Mongolia MNG 403 329
Singapore SGP 163 434 472
South Africa ZAF 683 450 348
Israel ISR 377 615 532
Pakistan PAK 628 712 573
Germany DEU 665 715 665
France FRA 786 772 862
Malaysia MYS 369 865 921
Hong Kong SAR, China HKG 386 968 1459
Egypt, Arab Rep. EGY 656 1148 234
China CHN 52 1235 2494
Australia AUS 1030 1355 1959
Korea, Rep. KOR 688 1518 1767
United Kingdom GBR 1874 2405 2179
Spain ESP 399 2986 3167
Japan JPN 2118 3058 3470
Canada CAN 1119 3756 3876
India IND 2781 5650 5191
United States USA 6699 5685 4102

Solutions

Expert Solution

x y (x-x̅)² (y-ȳ)² (x-x̅)(y-ȳ)
3 10 188287.93 196361.94 192282.56
5 17 186556.24 190207.15 188372.85
8 11 183973.71 195476.68 189638.00
11 20 181409.18 187599.39 184478.32
12 20 180558.34 187599.39 184045.20
13 7 179709.50 199029.70 189123.05
13 10 179709.50 196361.94 187851.28
14 6 178862.65 199922.96 189099.84
14 16 178862.65 191080.41 184870.63
18 24 175495.28 184150.37 179770.74
19 24 174658.44 184150.37 179341.62
22 13 172159.91 193712.17 182618.37
22 18 172159.91 189335.90 180543.76
23 9 171331.06 197249.19 183833.93
24 34 170504.22 175667.82 173066.76
24 102 170504.22 123290.49 144988.10
26 25 168856.54 183293.11 175926.80
27 47 168035.69 164939.51 166480.40
30 40 165585.16 170674.29 168110.47
31 37 164772.32 173162.06 168915.11
31 45 164772.32 166568.02 165667.74
31 64 164772.32 151420.17 157955.23
35 61 161540.95 153763.94 157604.48
38 37 159138.418 173162.055 166002.215
40 87 157546.732 134049.310 145323.882
42 36 155963.045 173995.310 164732.627
42 43 155963.045 168204.526 161968.176
46 29 152819.673 179884.095 165800.568
47 59 152038.830 155336.448 153678.794
48 51 151259.987 161706.487 156396.039
49 74 150483.143 143737.624 147071.715
51 33 148935.457 176507.075 162136.245
54 62 146628.928 152980.683 149771.137
55 76 145864.085 142225.114 144033.108
57 11 144340.398 195476.683 167973.755
57 57 144340.398 156916.957 150497.363
59 41 142824.712 169849.036 155751.853
62 31 140566.183 178191.585 158264.686
62 42 140566.183 169025.781 154140.549
63 46 139817.339 165752.761 152233.735
66 184 137582.8101 72429.58487 99825.17628
68 158 136103.1238 87100.21232 108878.8822
76 76 130264.3787 142225.1143 136113.4312
78 17 128824.6924 190207.1535 156535.5488
78 32 128824.6924 177348.33 151151.7253
83 101 125260.4767 123993.7417 124625.4998
85 189 123848.7905 69763.31036 92952.14687
91 70 119661.7316 146786.6437 132532.0488
96 124 116227.516 108324.879 112206.6469
98 216 114867.8297 56229.42801 80367.60765
99 1086 114190.9865 400527.6633 -213861.2845
114 76 104278.3395 142225.1143 121782.588
131 142 93588.00615 96800.29075 95180.59785
143 154 86389.8885 89477.23193 87920.00961
147 119 84054.51596 111641.1535 96870.75471
154 111 80044.61399 117051.1927 96795.2351
158 243 77797.24145 44153.54566 58609.07824
161 12 76132.71203 194593.428 121716.5782
166 131 73398.49635 103766.0947 87271.27432
179 184 66523.53556 72429.58487 69413.77432
180 105 66008.69243 121192.7221 89441.45079
184 198 63969.31988 65090.01624 64527.2351
193 174 59497.73164 77912.13389 68085.20569
195 192 58526.04537 68187.54566 63172.36255
196 276 58043.20223 31374.13389 42673.82334
202 213 55188.14341 57661.19271 56411.11745
216 844 48806.33948 152781.3496 -86352.17666
235 268 40772.31988 34272.17311 37381.2253
238 287 39569.79047 27598.32997 33046.33314
239 229 39172.94733 50233.11428 44359.65667
254 225 33460.30027 52042.13389 41729.43118
258 238 32012.92772 46279.82017 38490.94098
278 332 25256.06498 14671.85938 19249.76451
282 133 24000.69243 102481.5849 49594.64687
288 405 22177.6336 2316.251538 7167.215494
295 279 20141.73164 30320.36918 24712.44098
327 284 12082.75125 28604.09468 18590.75471
331 459 11219.3787 34.48683199 -622.029604
341 267 9200.947328 34643.42801 17853.63706
354 69 6875.986544 147553.8986 31852.45079
354 387 6875.986544 4372.839773 5483.391965
398 502 1514.888504 2388.526048 -1902.196271
399 353 1438.045367 10025.50644 3796.990004
403 329 1150.672818 15407.62409 4210.597847
434 472 8.535563245 356.1731065 -55.13744714
450 348 171.0453672 11051.78095 -1374.902153
615 532 31711.92772 6220.878989 14045.49981
712 573 75668.14341 14369.42801 32974.35275
715 665 77327.61399 44889.97703 58917.18608
772 862 112277.5552 167176.7613 137004.3724
865 921 183251.1434 218904.7221 200286.1469
968 1459 282044.3003 1011779.585 534197.2155
1148 234 505632.5356 48016.83977 -155816.8041
1235 2494 636929.1826 4165160.761 1628776.363
1355 1959 842868.0062 2267652.134 1382509.108
1518 1767 1168730.575 1726261.075 1420399.274
2405 2179 3873332.712 2978636.055 3396652.539
2986 3167 6497800.849 7365104.212 6917873.98
3058 3470 6870052.143 9101519.977 7907459.568
3756 3876 11016281.63 11716056.49 11360782.45
5650 5191 27176186.73 22447436.29 24698901.2
5685 4102 27542327.22 13314270.88 19149569.32
ΣX ΣY Σ(x-x̅)² Σ(y-ȳ)² Σ(x-x̅)(y-ȳ)
total sum 44566 46219 96279603.37 87281401.3 87903305.02
mean 436.92 453.13 SSxx SSyy SSxy

sample size ,   n =   102          
here, x̅ = Σx / n=   436.92   ,     ȳ = Σy/n =   453.13  
                  
SSxx =    Σ(x-x̅)² =    96279603.3725          
SSxy=   Σ(x-x̅)(y-ȳ) =   87903305.0          
                  
estimated slope , ß1 = SSxy/SSxx =   87903305.0   /   96279603.373   =   0.9130
                  
intercept,   ß0 = y̅-ß1* x̄ =   54.2179          
                  
so, regression line is   Ŷ =   54.2179   +   0.9130   *x
................

Predicted Y at X=   278   is                  
Ŷ =   54.21794   +   0.913000   *   278   =   308.032 = 308 (ROUND OFF)

predicted number of companies in 2012 for Sweden = 308

observed number of companies in2012 = 332

residual = 332 - 308 = 24

...........................

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.9589

please revert back for doubt

orchestra answered 3 years ago
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